Entanglement creation in a quantum-dot–nanocavity system by Fourier-synthesized acoustic pulses

We explore the possibility of entangling an excitonic two-level system in a semiconductor quantum dot with a cavity defined on a photonic crystal by sweeping the cavity frequency across its resonance with the exciton transition. The dynamic cavity detuning is established by a radio frequency surface acoustic wave (SAW). It induces Landau-Zener transitions between the excitonic and the photonic degrees of freedom and thereby creates a superposition state. We optimize this scheme by using tailored Fourier-synthesized SAW pulses with up to five harmonics. The theoretical study is performed with a master equation approach for present state-of-the-art setups. Assuming experimentally demonstrated system parameters, we show that the composed pulses increase both the maximum entanglement and its persistence. The latter is only limited by the dominant dephasing mechanism, i.e., the photon loss from the cavity.

Figure 1

(a) Semiconductor quantum dot placed in a photonic crystal, which serves as a realization for the cavity QED. Applying surface acoustic waves (SAWs) to the photonic crystal leads to a modulation of the cavity resonance frequency. (b) Energy spectrum of the system in dependence on the detuning $\Delta$. Owing to the cavity-QD coupling $g$, the exciton energy (black solid line) and the one-photon energy (red solid line) split at the degeneracy point $\Delta =0$ to form an avoided crossing (dotted lines). (c) Wave forms considered herein, which originate from a superposition of higher SAW harmonics.

Figure 2

LZ entanglement dynamics for SAW shapes of a pure sine with frequencies 1 GHz (a), 3 GHz (b), and 5 GHz (c), as well as for a spike (d), a sawtooth (e), and a square (f), each with fundamental frequency $\Omega /2\pi =1$ GHz. The cavity-dot coupling is $g=35\mu$eV, while the static detuning ${\Delta }_0=0.3$ meV is modulated with an amplitude $A=1$ meV, such that the crossing is reached at time $t_0=T/10=0.5$ ns. The cavity and exciton decay rates read ${\Gamma }_{\gamma }=25\mu \mathrm{eV}/\hslash$ and ${\Gamma }_X=0.2\mu \mathrm{eV}/\hslash$. Upper panels: Population of the states $|1_X,0_{\gamma }\rangle$ (red solid line) and $|0_X,1_{\gamma }\rangle$ (green dashed line). The dotted line visualizes the course of the detuning $\Delta \left(t\right)$. Lower panels: Cavity-dot entanglement in terms of the concurrence $\mathcal{C}$.

Figure 3

Maximum of the concurrence achieved as a function of the static detuning ${\Delta }_0$ and the dot-cavity coupling $g$. All other parameters, the wave forms, and the arrangement of the panels are as in Fig. 2.

Figure 4

Persistence of the entanglement, i.e., time during which the concurrence exceeds the threshold value set by $\mathcal{C}>1/2$. All parameters, wave forms, and the contour lines marking the maximum of the concurrence are as in Fig. 3. The unit of the color bar is in ps.